The generator matrix

 1  0  1  1  1 X+2  1  1 2X 3X+2  1  1  1  1  1  1  0
 0  1 X+1 X+2 2X+3  1 2X+1  0  1  1 X+1  1 3X+2 2X  3 3X+1  1
 0  0 2X+2  0  0 2X 2X 2X+2 2X+2  2  2 2X 2X 2X+2  2  0  2
 0  0  0  2 2X 2X+2  0  2 2X 2X+2 2X+2  2 2X 2X  0 2X+2  2

generates a code of length 17 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+164x^14+384x^15+937x^16+1152x^17+922x^18+384x^19+128x^20+16x^22+6x^24+2x^26

The gray image is a code over GF(2) with n=136, k=12 and d=56.
This code was found by Heurico 1.16 in 81.7 seconds.